Here is an example of how one can go camping alone, with only a bike to carry gear. This cyclist went to Lake Leschenaultia in Washington state. The cyclist packed his panniers full of camping equipment and food, cycled nearly 100 miles from his home to his camp grounds, pitched a tent and spent the night.
I feel as though a lot of people don't even think it is possible to camp at a camp ground with only the equipment your bike can carry. The reality is that driving a car to a camping ground kind of kills the spirit of camping itself. Living, working, and surviving on your own accord is a major part of camping, and a bicycle only adds to that.